A characterization of compactly supported orthonormal wavelets

J. Schneid

doi:10.1007/bf01955876

A characterization of compactly supported orthonormal wavelets

BIT Numerical Mathematics ◽

10.1007/bf01955876 ◽

1994 ◽

Vol 34 (2) ◽

pp. 295-303 ◽

Cited By ~ 1

Author(s):

J. Schneid

Keyword(s):

Compactly Supported ◽

Orthonormal Wavelets

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Continuity of Convolution of Test Functions on Lie Groups

Canadian Journal of Mathematics ◽

10.4153/cjm-2012-035-6 ◽

2014 ◽

Vol 66 (1) ◽

pp. 102-140

Author(s):

Lidia Birth ◽

Helge Glöckner

Keyword(s):

Continuous Functions ◽

Locally Convex Space ◽

Locally Compact Group ◽

Locally Convex Spaces ◽

Test Functions ◽

Bilinear Map ◽

Locally Compact ◽

Compactly Supported ◽

Locally Convex

AbstractFor a Lie group G, we show that the map taking a pair of test functions to their convolution, is continuous if and only if G is σ-compact. More generally, consider with t ≤ r + s, locally convex spaces E1, E2 and a continuous bilinear map b : E1 × E2 → F to a complete locally convex space F. Let be the associated convolution map. The main result is a characterization of those (G; r; s; t; b) for which β is continuous. Convolution of compactly supported continuous functions on a locally compact group is also discussed as well as convolution of compactly supported L1-functions and convolution of compactly supported Radon measures.

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ORTHONORMAL MRA WAVELETS: SPECTRAL FORMULAS AND ALGORITHMS

International Journal of Wavelets Multiresolution and Information Processing ◽

10.1142/s021969131100450x ◽

2012 ◽

Vol 10 (01) ◽

pp. 1250008 ◽

Cited By ~ 1

Author(s):

F. GÓMEZ-CUBILLO ◽

Z. SUCHANECKI ◽

S. VILLULLAS

Keyword(s):

Multiresolution Analysis ◽

Matrix Representation ◽

Infinite Product ◽

Scaling Functions ◽

Compactly Supported ◽

Orthonormal Bases ◽

Spectral Decompositions ◽

Product Matrix ◽

Orthonormal Wavelets

Spectral decompositions of translation and dilation operators are built in terms of suitable orthonormal bases of L2(ℝ), leading to spectral formulas for scaling functions and orthonormal wavelets associated with multiresolution analysis (MRA). The spectral formulas are useful to compute compactly supported scaling functions and wavelets. It is illustrated with a particular choice of the orthonormal bases, the so-called Haar bases, which yield a new algorithm related to the infinite product matrix representation of Daubechies and Lagarias.

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